SLIDING-BLOCK BACK ANALYSES OF LIQUEFACTION-INDUCED SLIDES

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1 3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 004 Paper No. 309 SLIDING-BLOCK BACK ANALYSES OF LIQUEFACTION-INDUCED SLIDES Constantine A. STAMATOPOULOS and Stavros ANEROUSSIS, SUMMARY Sliding system models where the slide consists of parts sliding in different inclinations have been proposed (Stamatopoulos et al, 000, Sarma and Chlimitzas, 000). These models simulate changes of geometry of the soil mass with the distance moved towards a gentler configuration, that greatly affect the seismic displacement when this displacement is large. The two-body model that was proposed by Stamatopoulos et al (000), even simplified simulates with reasonable accuracy the displacement of both the upper and the lower part of liquefaction-induced slides of small dams and embankments. Yet, the Stamatopoulos et al (000) model assumes only cohesional resistance. It is applicable when the undrained soil strength is mobilized everywhere. In cases of earthquake-induced failures of dams and embankments, often the lower part of the slip surface is below the water level, and liquefies, but the upper part is above the water table and does not liquify. In the paper, the Stamatopoulos et al (000) sliding system model is extended to include both frictional and cohesional components of resistance in order to be able to simulate the slides described above. Then, the modified model is used to back-estimate the residual shear strength of four slides of small dams and embankments. Finally, the correlation of the residual soil strength and the blow count resistance of the SPT of these cases is compared to the relationships that have been proposed by Seed and Harder (990) and Ishihara (993).. INTRODUCTION During recent earthquakes, small dams and embankments were badly damaged as a result of earthquakes (e.g. Stamatopoulos, 003). The excessive deformation of these earth structures was a result of liquefaction within the earth structures, or at the top of the underlain soil. Some of these case studies are well-documented: the initial and deformed geometries have been recorded, and field standard penetration tests were performed. Characteristics of the applied earthquake are also known. Stamatopoulos and Associates Co., 5 Isavron street, Athens 4-7, Greece, kostama@athena.compulink.gr

2 Analysis of such slides provides a unique opportunity to correlate the blow count resistance of the Standard Penetration Test (SPT) to the residual strength of a liquefied soil. Evaluation of the residual strength of a liquefied soil is one of the most difficult problems in contemporary geotechnical engineering practice, mainly because it is difficult to obtain undisturbed samples in sands. Approaches have been developed to relate the shear strength of liquefied soils to the SPT blow count resistance: Seed and Harder (990) give a range of the shear strength of liquefied soils, c u, while Ishihara (993) gives a lower bound of the ratio of the shear strength and the consolidation vertical stress c u /σ' v in terms of the corrected blow count of the SPT. The relations of Seed and Harder (990) and Ishihara (993) are probably based on stability analyses of the initial and final slide configurations assuming a safety factor equal to, and/or analyses using the sliding-block model (Newmark, 965). However, the factor of safety exactly before the slide is less than one because motion develops; after the slide it is greater than one, as a result of inertia. In addition, the conventional sliding-block model has shortcomings in back-estimating the soil strength of earthquakeinduced slides when seismic displacement is large. The reason is that the change on geometry of the sliding mass, that greatly affects the seismic displacement, is not modeled. To overcome the above problems, sliding system models, where the slide consists of parts sliding in different inclinations have been proposed (Stamatopoulos et al, 000, Sarma and Chlimitzas, 000). The model by Stamatopoulos et al (000) consists of two sliding bodies, while the model of Sarma and Chlimitzas (000) of "n" sliding bodies. For soil to move along the (external) lines with different inclinations, internal shearing must be allowed along lines intersecting the angle between the external lines. This internal sub-plane(s) together with the external sub-planes define the bodies of these sliding system models. Mass of the upper bodies is transferred to the lower bodies as the sliding system moves downwards. The stress state along the internal lines must be at failure (Sarma, 979). The -body model by Stamatopoulos et al (000) has been used to analyze dam slides triggered by the 97 San Fernando earthquake and by the 985 Chilean earthquake (Stamatopoulos et al, 000) and the seismic displacement of the mole embankment at King Harbor Redondo Beach as a result of the Northridge earthquake of 994 (Stamatopoulos and Aneroussis, 004). These analyses have illustrated that this sliding system model, even simplified, simulates with reasonable accuracy the displacement of both the upper and the lower part of the slides. Yet, further study of case histories of earthquake-induced slides of a number of slides of dams and embankments has illustrated that in many cases the lower subplane is below the water level and liquefies, but the upper part is mainly above the water table and/or does not liquify. The Stamatopoulos et al (000) model assumes only cohesional resistance at both the external sub-planes and the internal sub-plane. It is applicable when the undrained soil strength is mobilized at both the upper and lower sub-planes by using the undrained soil strength in place of the resistance. Thus, it cannot be used for the case described above. It is inferred that a practical sliding system model that simulates with reasonable accuracy the seismic displacement of the slides described above is the two-body model that includes both frictional and cohesional components of resistance. In the present paper such a model is formulated. Then, it is used to back-estimate the residual shear strength of four slides of small dams and embankments. Finally, the correlation of the residual soil strength and the blow count resistance of the SPT is compared to the relationships that have been proposed by Seed and Harder (990) and Ishihara (993).

3 . THE MODEL General The -dimensional mass sliding as a result of a horizontal earthquake on two sub-planes, shown in Fig., is considered. An internal sub-plane separates the two bodies. Thus, two bodies can be defined sliding in two inclinations: body sliding at the gentler inclination and body at the steeper. The shape of the top (ground) surface of body can be defined with successive segments and this is necessary because these geometric particularities affect the mass transfer between the two bodies. Yet, as in the cases histories that will be studied, the top of the part of body that changes inclination consists of only one segment, only the inclination of this first segment will be specified. The parameters that define the model and affect the solution can be separated into (a) the inclinations of the two external and the internal sub-planes, (b) the initial masses and weights of the two bodies, (c) other factors of the initial geometry, (d) the resistance along the external and internal slip sub-planes and (e) the total and effective unit weights of the mass that changes inclination, γ t and γ b. Specifically referring to Figs and, we must define (a) the inclinations of the external sub-planes where the two bodies slide, α and α, and the inclination of the internal sub-plane, 90 o -δ, (b) the initial masses and weights of the two bodies m ο, m ο and W o, W o, (c) the initial contact lengths, b o and b o, the initial length of the internal sub-plane, d o, and the inclination of the first segment of the top body relative to α, θ, (d) the frictional and cohesional resistance along the external and internal sub-planes, φ, φ, φ' and c, c, c', where the tone corresponds to the internal sub-plane and (e) the total and effective unit weights of the mass changing inclination, γ t and γ b. Finally, the distances moved along the first and second slip sub-planes are defined as u and u respectively. The proposed model assumes that the angle of the internal sub-plane of the slide, δ, is constant and does not change as a function of the distance moved. In addition, the -dimesional total mass of the slope is taken to be constant throughout the sliding period. Thus, at each time increment the incremental change in cross-sectional area of body should equal the change of area of body, or, d(t) du (t) sin(90 o +δ +α )= d(t) du (t) sin(90 o +δ +α ) (a) where d indicates incremental change and (t) denotes function of time. This gives that: (b) u / u = du / du = cos(δ +α ) / cos(δ +α ) = λ or, that the ratio of displacements moved along the two slip lines depends only on the relative inclinations of the external slip lines and the line of internal shearing. 3

4 (a) θ-(l+)+α θ-+α A-O, m -O, W-O θ-+α A-O, m -O, W-O d(=do) b - b- b -l b 0 cosα b0 cosα (b) Α m= Α-γt/g W= Α-γ A-O, m -O, W-O do θ-+α d(t) θ-+α θ-(l+)+α Α=Α-ο- Α m =m-ο- Αγt/g W=W-ο- Α-γ b --u u b--u b -l-u b0 cosα=(b0 +u )cosα b 0 cosα=(b0 -u )cosα Fig.. Sliding system considered : (α) Initial position, (b) position when the distance moved by the second body is u (Note that u < b - ). kmg W kmg φ' Pa Pa φ' c' d cb+n tanφ N W c' d cb+n tanφ N Fig.. Forces on bodies and : (a) Body, (b) Body. 4

5 The governing equation of motion. Fig. gives the exerted forces in the two bodies. The equation of motion of body in the direction of sliding is: m ( d u / dt ) = cosφ c b [ m g sin cosφ c' ( α φ ) + P cos( φ' + φ α δ ) d sin ( φ δ α ) + kw cos( α φ )] a (a) where g is the acceleration of gravity, {g k} is the applied acceleration and the other parameters were defined previously. Note that the weight W is not always equal to the product {m g}, since in the case of submerged mass, it corresponds to the buoyant weight. Similarly, the equation of motion of body in the sliding direction is: m ( d u / dt ) = [ m g sin( α φ ) Pa cos( φ' + φ α δ ) cosφ (b) c b cosφ + c' d sin φ δ α + kw cos α φ ( ) ( )] Combination of the above equations, and using equation () relating the incremental distance moved by the two bodies, gives that the governing equation of the sliding system is: (d u /dt ) = Z g ( k(t) k c ) (3a) where, m cos ( ) ( α φ ) m cos α φ + µ Z = (3b) m cosφ m cosφ + λµ AA k c = with (3c) BB AA= W sin (φ -α ) + c b cos φ + c' d sin (φ -δ -α ) + (W sin (φ -α ) + c b cos φ - c' d sin (φ -δ -α ) )/ µ (3d) BB= m sin( α φ ) m sin ( α φ ) + (3e) µ where µ = cos(φ' +φ -δ -α ) / cos(φ' +φ -δ +α ) (3f) The change of the lengths, masses and weights To solve equation (3), we need to express b, b, W, W, m, m, d, as a function of the distance moved, u. The change of the lengths and cross-sectional area of the second body is b = b 0 - u / λ (4) 5

6 d sinθ sinθ = d 0 + u = d 0 + (5) cos( θ + α + δ ) cos( θ + α + δ ) λ Α = u cos( α + δ ) 0.5 cos( α + δ ) sinθ + u d 0 λ cos( θ + α + δ ) λ (6) For the slides that will be considered in the present work, the lower slip sub-plane is about horizontal. Thus, there is room in order the lower slip sub-plane to increase by u. It is inferred that the change of length and cross-sectional area of the first body are b = b 0 + u Α =- Α (7) Finally, the changes in masses and weights of the two bodies is W i = Α i γ m i = Α i γ t / g (8) where i takes the values of and and γ=γ b below the water table line and γ=γ t above the water table line. Discussion A computer program using the language fortran solving numerically the above equations was written. This computer program is used in the analyses below. The model is recommended only for back analyses of slides. In such cases the model parameter δ can be obtained from the distance moved along the two slip sub-planes and the compatibility condition (b). At this point it can be noted that according to the theory of limit equilibrium, the angle δ corresponds to that giving the minimum value of the critical acceleration, k c (Sarma, 979). In addition, δ does not necessarily have to be constant: as the body slides the relative masses of the two bodies change and the inclination of the interslice line producing a minimum critical acceleration can change. It is beyond the scope of the paper to simulate these effects on the value of δ, which is taken as being constant during the mass movement. As a check, in the case studies given later, the angle δ obtained from the distance moved is compared with that obtained from the limit equilibrium condition at the initial slide configuration. u 3. SLIDES THAT WILL BE BACK-ANALYZED Four well-defined -dimensional slides, where a large part of the slope is above the water table line, but the lower part of the slip surface is submerged were found in the literature. Their cross-sections are given in Fig 3. They are described below. La Marquesa Downstream and La Palma Dam Slides (De Alba et al, 988) La Marquesa Dam and La Palma Dam were subjected to large ground accelerations by the Chilean earthquake of March 3, 985, that had a surface wave magnitude M s of 7.8. La Marquesa Dam was located 45 km from the earthquake epicenter and the peak acceleration on site was estimated around 0.6g. La Palma Dam was located 75 km from the earthquake epicenter and the peak acceleration in the vicinity of the dam reached 0.46g. Major sliding of both the upstream and downstream slopes of the La Marquesa Dam took place (Fig. 3a). The maximum horizontal displacement measured at the downstream slope was about 5m. There also was a m loss of freeboard and extensive longitudinal cracking. The average measured post-earthquake 6

7 equivalent clean sand value of the SPT, N (60), of the silty sand layer of the downstream slope that liquefied was 9 (De Alba et al., 988). Major sliding of the upstream slope of La Palma Dam also occurred (Fig. 3b). The maximum horizontal displacement measured was 5m. In addition, considerable longitudinal cracking was observed. The average measured post-earthquake equivalent clean sand values of N (60) of the silty sand layer that liquefied was 3 (De Alba et al., 988). Embankment of Kushiro river (Kaneko et al, 995) The Kushiro-Oki Earthquake of magnitude 7.8 occurred in Hokkaido, the northern island of Japan, on January 5, 993. Along the Kushiro River on alluvial lowlands, dikes were given deadly blows in a long extent, while the peripheral surface (marsh and farmland) showed neither conspicuous breakage nor sand eruption. A peat bed of 3 to 6 m thickness spreads over alluvial lowlands of the Kushiro River. The peat bed was underlain by a sand bed and a thick soft marine clay bed. River levee with its height of 5 to 7 m had sank to 3m into the peaty bed prior to the earthquake. Materials of the levee are generally sandy soil originated from volcanic ashes. Dike material below the ground surface was submerged under ground water and was potentially liquefiable. Fig. 3c shows a sketch of failure of the Kushiro River dike. The failures are caused by liquefaction of dike materials sank into peat bed. The average SPT N value of the dike material under water table was 5. Peak accelerations were estimated as approximately 0.35g. Embankment of Rimnio river (Tika and Pitilakis, 999) The Kozani-Grevena earthquake of magnitude 6.0 occurred on May 3, 995, in North-Western Greece. The most impressive geotechnical damage observed was the failure of the Rimnio bridge embankment. During the earthquake, the embankment suffered serious damage. The pavement to a great length settled by to m, while according to a survey carried out after the earthquake, the maximum horizontal displacement was of the order of 0.8 to m, depending on the location (Fig. 3d). An extensive geotechnical investigation was carried out after the earthquake. The geotechnical investigation showed that the embankment is constructed from compacted clayey-sandy gravel and it is founded on a 3.5 to 4 m thick layer of loose silty sand, which extents beyond the embankment toe. Then follows a 7.5 m thick layer of dense sandy gravel and cobbles and a layer of marly clay. The latter extends to the bedrock with an increasing stiffness. The minimum number of SPT blows measured at the silty sand layer ten days after the earthquake was N SPT = 8. The corresponding (N ) 60 value equals to 4. Also, the piezometric ground water table at the silty sand layer at the same date was 4 m above the pavement, indicating the existence of a significant yet undissipated excess pore water pressure. Surficial effects of liquefaction, such as sand boils, were observed. These field observations indicated that failure was induced by the liquefaction of the silty sand layer. Futhermore, the maximum applied acceleration during the earthquake outside the region that liquified was about 0.7g. 7

8 Fig. 3. The slides studied in the present work: (a) the downstream slope of the La Marquesa Dam (De Alba et al, 988), (b) the La Palma Dam (De Alba et al, 988), (c) the embankment of Kushiro river (Kaneko et al, 995) and (d) the embankment of Rimnio river (Tika and Pitilakis, 999). 8

9 Undrained monotonic triaxial test (CU) on the silty sand gave for consolidation stress σ c =4kPa, an undrained residual strength c us of 6. to 33. kpa; the corresponding ratio c us /σ ν, where σ ν is the vertical stress perpendicular to the slip surface prior to shearing, equals to 0.49 to 0.88, assuming that the sand is normally-consolidated. 4. BACK-ANALYSES Model Geometries The methodology that was used to select the model geometries simulating the slides described above was the following: - The lower slip sub-plane was taken on the base of the embankments with inclination consistent to the failure mechanism. The location and inclination of the upper slip sub-plane was estimated based on the theory of limit equilibrium, as the sub-plane that corresponds to the minimum value of the critical acceleration. No data exists on the unit weight of the soil. A reasonable assumption, used in the analysis, is that the total unit weight of the soil, γ t, equals to t/m 3. - In order to finalize the model geometry, the inclination of the internal slip surface must be determined. This inclination was determined based on the ratio of the measured displacement of the upper and lower external sub-planes, using equation (b), as given in table. Based on all of the above, Fig 4 gives the initial geometry of the model slides. In addition, all the parameters (except those of the soil strength) defining the model slides are given in Table. Results In sliding-block analyses the applied acceleration corresponds to the average acceleration along the slip surface (e.g. Kramer, 996). The peak horizontal acceleration that has been measured, or estimated, at, or near, the slip surface by the scientists who studied the slides, are given it table 3. Different accelerograms, normalized at the maximum accelerations of table, were applied to investigate the effect of the applied accelerogram on the back-figured undrained soil strength. The following accelerograms covering a wide range of fundamental period and earthquake magnitude values for possible earthquakes were considered: - Port Island (Kobe, Japan), 7//995, component East-West at depth 6m., M(=earthquake magnitude)= 7., R(=distance from the epicenter)= 5 Km, a m (=maximum value of the acceleration) = 0.35g, T f (=fundamental period)=0.7 s. - El-Centro (California, USA), 8/5/940, component North-South, M= 6.5, R=5 Km, a m = 0.35g, T f =0.6 s. - San Fernando - Avenue of Stars (California, USA), 97, component East-West, M=6.5, R=40 Km, a m =0.5g, T f =0.5 s. - Kalamata (Greece), 3/9/986, M=5.75, R=9 Km, Municipality Building, longitudinal component: a m =0.4g, T f =0.35s - Gazli (former USSR), 7/5/976, M=7.3, a m =0.70g, T f =0. s. Above the water table, and/or at the region where liquefaction does not occur, a residual friction angle of 30 o and zero cohesional resistance is assumed for the sandy soil. An exception is the Rimnio embankment, where, as the upper part of the slides is partly submerged, to account for generation of excess pore pressures it is assumed that φ' =5 ο. Using back analysis, the sand strength c u of the soil below the water table that corresponds to the measured seismic displacement was estimated. 9

10 (a) (b) (c) (d) Fig. 4. The simulation of the initial geometries of the slides of Fig 4 with the proposed model: (a) the downstream slope of the La Marquesa Dam, (b) the La Palma Dam, (c) the embankment of Kushiro river and (d) the embankment of Rimnio river. 0

11 Thus, the model parameters c and c' are taken zero, while φ and φ' are taken 30 ο or 5 o. The model parameter c is taken equal to c u, while φ is taken zero. The sand strength c u was first estimated for the Port Island input motion, as given in table 3. Table 3 also gives the back-estimated values of c u /σ' for all slides considered. The average vertical stress at the slip sub-plane that liquifies, σ', was estimated according to Olson et al (000) as σ'= Σ(l i σ' i ) / Σl i (9) where l i is the length of the slip surface where the vertical effective stress equals σ' i. The value of the critical acceleration at the initial configuration of the slides predicted in the above analyses is also given in table 3. It can be observed that the large measured slope displacements correspond to negative critical acceleration value. Negative critical acceleration value indicates static instability. The back-estimated residual soil strength in terms of the applied accelerogram are given in table 4a. It can be observed that the effect of the applied accelerogram on the back-estimated residual soil strength is small, presumably because most of the seismic displacement is a result of static instability (due to earthquake-induced loss of strength). The effect of the soil strength of the sandy soils above the water table and/or at the region that does not liquify was also investigated. The frictional resistance of the sandy soils above the water table varied from 5 0 to 35 o. The back-estimated residual soil strength, in terms of the soil strength of body is given in table 4b. It can be observed that as the soil strength increases, the back-estimated residual soil strength of body decreases. Correctness of the analyses According to the theory of limit equilibrium, the internal sub-plane must correspond to the minimum value of the critical acceleration (Sarma, 979). Fig 5 gives the critical acceleration in terms of the inclination of the internal sub-plane at the initial slide configuration. The values of soil strength used in the analyses are similar to those back-estimated above. Table gives the angle δ obtained from Fig. 5 according to the limit equilibrium condition. It can be observed that the range of the angles δ, that produce a minimum in the critical acceleration is within about 5 o of the value of δ from the ratio u /u. The above illustrates the validity of the proposed approach. As described above, in the case of the Rimnio embankment the undrained soil strength was estimated by triaxial constant-volume tests by Tika and Pitilakis (999). The measured ratio c u /σ' v was 0.5 to 0.9. Based on table 3, the back analysis gave for the case of Rimnio, a c u /σ' ratio equals to 0.6. Comparing this value with the measured ratio c u /σ' v, it can be observed that it agrees.

12 Table. Relative displacement along the two slip sub-planes and corresponding angle δ. The value of critical acceleration based on the analysis of Fig 5 is also given. Case u u δ -kinematic δ -stabiliy La Marquesa Dam downstream La Palma dam Embankment of Kushiro river Embankment of Rimnio river Table. The model parameters for each case Case α, α ( o ) m g, m g (kpa) W, W (kpa) b, b, d (m) δ, θ ( ο ) La Marquesa Dam 0, 45.4, , , 5.4, , -0 downstream La Palma dam 0, , , , 4.0, 4.8-4, - Embankment of Kushiro 0, , , , 9.4, 4.9 -, - Embankment of Rimnio 0, 7 4., , ,.4, , -43 Table 3. The maximum applied horizontal acceleration, and undrained strength that was back-estimated for each case. The corresponding critical acceleration is also given. The Hyogoken-Nambu Quake was applied and a frictional resistance of 30 o was assumed for body, except for the Rimnio embankment case, where a frictional resistance of 5 o was assumed. Case a max (g) a co (g) c u (kpa) σ' v (kpa) c u / σ v La Marquesa Dam downstream La Palma dam Embankment of Kushiro river Embankment of Rimnio river Table 4. Parametric analyses. Effect of the applied accelerogram on the back-estimated residual soil strength (a) in terms of the applied earthquake Case Port Island Quake El- Centro Quake San Fernando Quake Kalamata quake Gazli quake La Marquesa Dam downstream La Palma dam Embankment of Kushiro river Embankment of Rimnio river (b) in terms of the frictional resistance above the water table line (Hyogoken-Nambu quake) Case φ=5 ο φ=30 ο φ=35 ο La Marquesa Dam downstream La Palma dam Embankment of Kushiro river Embankment of Rimnio river

13 Critical Acceleration Coefficient (kc) Marquesa - Downstream (C=0 kpa, Φ=Φ'=30 deg.) Palma - Upstream (C=0 kpa, Φ=Φ'=30 deg.) Kushiro (C=3.5 kpa, Φ=Φ'=30 deg.) Rimnio (C=0 kpa, Φ=Φ'=5 deg.) Interface Angle (deg.) Fig. 5. Critical acceleration in terms of inclination of internal sub-plane. 5. THE UNDRAINED SOIL STRENGTH IN TERMS OF N (60) Table 5 gives the measured N (60) value of all slides analyzed. In addition, it compares (a) the backestimated value of the undrained soil strength c u of Fig. 3 with the range of values proposed by Seed and Harder (990) for the measured N (60) value, and (b) the back-estimated value of the ratio c u /σ' of Fig. 3 with the lower bound proposed by Ishihara (993) for the measured N (60) of all slides analyzed. It can be observed that the pairs of N (60) and the corresponding back-estimated c u and c u /σ' values are within the range proposed by Seed and Harder and the lower bound proposed by Ishihara. An exception is the Rimnio embankment where the back-estimated c u is less than the proposed bounds by Seed and Harder. In addition, the pairs show a more-or-less increase of c u with N (60). An exception is the La Palma Dam. Statistical analysis of the data is not performed, as the number of pairs is small. 6. CONCLUSIONS In the paper, a two-body system model is extended to include both frictional and cohesional components of resistance. In this way, slides where the lower sub-plane of the slip surface is below the water level, and liquefies, but the upper part is above the water table and/or does not liquify can be simulated in a simplified manner. Then, the model is used to back-estimate the residual shear strength of four slides of small dams and embankments with the characteristics described above. This study illustrated that the two-body model simulates with reasonable accuracy the kinematics of a number of liquefaction-induced slides. In addition, it illustrated that as soil displacement was primarily caused by static instability (due to earthquake-induced loss of strength), the applied accelerogram does not affect the results considerably. Finally, the pairs of the back-estimated c u values and the corresponding N (60) values are more-or-less within the range of values proposed by Seed and Harder (990) and the lower bound proposed by Ishihara (993). 3

14 Table 5. Measured N (60) value of the Standard Penetration Test and corresponding (a) limits of c u according to Seed and Harder (990) and (b) the lower bound of c u /σ' v according to Ishihara (993). Whether the back-estimated c u value is within the limits and lower bound is assessed Case Ν (60) Seed and Harder limits of c u (kpa) Is backestimated c u within the limits? Ishihara lower bound of c u /σ' v La Marquesa Dam 9 - Yes 0.04 Yes downstream La Palma dam 4-0 Yes 0 Yes Embankment of Kushiro 5 0- Yes 0 Yes river Embankment of Rimnio river No 0. Yes Is backestimated c u /σ' within the lower bound? 7. ACKNOWLEDGMENTS This work was supported by the Hellenic Organization of Seismic Protection (OASP) during 00 and REFERENCES. European Prestandard. Eurocode 8 - Design provisions of earthquake resistance of structures - Part 5: Foundations, retaining structures and geotechnical aspects, Ishihara, K. Liquefaction and Flow Failure During Earthquakes", 33rd Rankine Lecture, Gιotechnique 43, No. 3, 993, pp Kaneko M., Sasaki Y., Nishikawa J., Nagase M., Mamiya K.: River Dike Failure in Japan by Earthquakes in 993, Proceedings: Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, 995, Vol I, pp Kerwin S. T., Stone J. J. Liquefaction, failure and remediation: King Harbor Beach, California Journal of Geotechnical and Geoenvironmental Engineering, 997, Vol. 3, No Kramer, S.L. "Geotechnical Earthquake Engineering", Prentice Hall, New Jersey, ?ewmark, N. M. Effect of earthquakes on dams and embankments, Geotechnique, Vol. 5, No., London, England, June, 965, pp Olson S. M, Stark T. D., Walton W. H., Castro G 907 static liquefaction flow failure of the Noth Dike of Wachusett Dam, Journal of Geotechnical Engineering, 000, Vol. 6, No.. 8. Sarma S.K. Stability analysis of embankments and slopes, Journal of Geotechnical Engineering ASCE; 979, Vol.05, No., pp Sarma, S. K. and Chlimitzas G. Edited Report # for the project Seismic Ground Displacements as a tool for town planning, design and mitigation, Seed R. B. and Harder L. F. SPT-based analysis of cyclic pore pressure and undrained residual strength. Proc. H. B. Seed Memorial Symp, Bi-Tech Publishing Ltd., Richmond, British Columbia, 990, Vol, pp Seed H.B., Lee K. L., Idriss I. M., Makdisi F. I.: The slides in the San Fernando Dams during the earthquake of February 9, 97, Journal of Geotechnical Engineering ASCE, 975, Vol. 0, No. 7, pp

15 . Stamatopoulos C., Velgaki E. and Sarma S. Sliding-block back analysis of earthquake-induced slides, Soils and foundations, The Japanese Geotechnical Society, 000, Vol. 40, No. 6, pp Stamatopoulos C. Collection-analysis of permanent seismic deformations and improvement of the seismic code, Final report, Hellenic Organization of aseismic propection (OASP), Athens, Greece, Stamatopoulos C. and Aneroussis S. Back analysis of the liquefaction failure at King Harbor Redondo Beach, California, Fifth International conference on case histories in Geotechnical Engineering, New York, NY, 004, April 3-7 (in press). 5. Tika T.E. and Pitilakis K.D. Liquefaction Induced Failure of a bridge embankment, Proceedings: Proceedings of the Second International Conference on Earthquake Geotechnical Engineering, Balkema, 99, pp

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